The Nichols algebra $\mathfrak{B}(V_{abe})$ and a class of combinatorial numbers

TL;DR

This paper studies a specific Nichols algebra from the Yetter-Drinfeld category of Suzuki algebras, revealing new constructions and connecting it to combinatorial numbers related to symmetric groups.

Contribution

It introduces a new method to obtain certain Nichols algebras and establishes a novel link between these algebras and combinatorial numbers on symmetric group subgroups.

Findings

Reconstructed 4n and n^2 dimensional Nichols algebras using a different approach.

Established a connection between Nichols algebras and combinatorial numbers.

Provided new insights into the structure of Nichols algebras from Suzuki algebras.

Abstract

We investigate the Nichols algebra $\mathfrak{B}(V_{abe})$ which are from the Yetter-Drinfeld category of Suzuki algebras. The $4n$ and $n^2$ dimensional Nichols algebras, first appeared in \cite{Andruskiewitsch2018}, are obtained again via a different method. And the connection between the Nichols algebra $\mathfrak{B}(V_{abe})$ and a class of combinatorial numbers on the subgroups of symmetric groups is established.